If you’ve been running your WordPress site for a while then there may well be lots of junk in your core wp-options table. If you add an index to the autoload table you can often see a dramatic improvement in response time. You’ll need mysql/phpmyadmin access so only give it a go if you know what you’re doing!
ALTER TABLE `wp_options`
ADD INDEX `auto_idx` USING BTREE (`autoload` ASC);